Question

If sin⁻¹x+sin⁻¹x=2π/3, then cos⁻¹x+cos⁻¹y=......,Select Proper option from the given options.
(a) π/6
(b) π/3
(c) π/4
(d) π

Answer 1

In the attachment I have answered this problem.     Option (b) is correct.     See the attachment for detailed solution.  

Answer 2

we know, a very important formula,
$\qquad\bf{sin^{-1}P+cos^{-1}P=\frac{\pi}{2}}$
where |P| ≤ 1

so, sin^-1x + cos^-1x = π/2 .......(1)
and sin^-1y + cos^-1y = π/2 ...........(2)

now Given, sin^-1x + sin^-1y = 2π/3

π/2 - cos^-1x + π/2 - cos^-1y = 2π/3 [from equations (1) and (2), ]

π - [cos^-1x + cos^-1y] = 2π/3

π - 2π/3 = cos^-1x + cos^-1y

cos^-1x + cos^-1y = π/3

hence, option (b) is correct